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Searching for quantum optimal control fields in the presence of singular critical points

Author(s): Riviello, Gregory; Brif, Constantin; Long, Ruixing; Wu, Re-Bing; Tibbetts, Katharine Moore; et al

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Abstract: Quantum optimal control has enjoyed wide success for a variety of theoretical and experimental objectives. These favorable results have been attributed to advantageous properties of the corresponding control landscapes, which are free from local optima if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is full rank, and (3) the control field is not constrained. This paper explores how gradient searches for globally optimal control fields are affected by deviations from assumption (2). In some quantum control problems, so-called singular critical points, at which the Jacobian is rank deficient, may exist on the landscape. Using optimal control simulations, we show that search failure is only observed when a singular critical point is also a second-order trap, which occurs if the control problem meets additional conditions involving the system Hamiltonian and/or the control objective. All known second-order traps occur at constant control fields, and we also show that they only affect searches that originate very close to them. As a result, even when such traps exist on the control landscape, they are unlikely to affect well-designed gradient optimizations under realistic searching conditions.
Publication Date: 7-Jul-2014
Citation: Riviello, Gregory, Brif, Constantin, Long, Ruixing, Wu, Re-Bing, Tibbetts, Katharine Moore, Ho, Tak-San, Rabitz, Herschel. (2014). Searching for quantum optimal control fields in the presence of singular critical points. PHYSICAL REVIEW A, 90 (10.1103/PhysRevA.90.013404
DOI: doi:10.1103/PhysRevA.90.013404
ISSN: 1050-2947
EISSN: 1094-1622
Pages: 013404-1 - 013404-12
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW A
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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